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Convergence of an adaptive finite element method for distributed flux reconstruction


Authors: Yifeng Xu and Jun Zou
Journal: Math. Comp. 84 (2015), 2645-2663
MSC (2010): Primary 65N12, 65N21, 65N30
DOI: https://doi.org/10.1090/mcom/2961
Published electronically: April 17, 2015
MathSciNet review: 3378842
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Abstract: We shall establish the convergence of an adaptive conforming finite element method for the reconstruction of the distributed flux in a diffusion system. The adaptive method is based on a posteriori error estimators for the distributed flux, state and costate variables. The sequence of discrete solutions produced by the adaptive algorithm is proved to converge to the true triplet satisfying the optimality conditions in the energy norm, and the corresponding error estimator converges to zero asymptotically.


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Additional Information

Yifeng Xu
Affiliation: Department of Mathematics, Scientific Computing Key Laboratory of Shanghai Universities — and — E-Institute for Computational Science of Shanghai Universities, Shanghai Normal University, Shanghai 200234, China
Email: yfxu@shnu.edu.cn

Jun Zou
Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Email: zou@math.cuhk.edu.hk

DOI: https://doi.org/10.1090/mcom/2961
Keywords: Distributed flux reconstruction, adaptive finite element method, convergence
Received by editor(s): June 23, 2013
Received by editor(s) in revised form: February 11, 2014
Published electronically: April 17, 2015
Additional Notes: The research of the first author was partly supported by NSFC (11201307), MOE of China through Specialized Research Fund for the Doctoral Program of Higher Education (20123127120001), E-Institute of Shanghai Universities (E03004), Innovation Program of Shanghai Municipal Education Commission (13YZ059)
The work of the second author was supported by Hong Kong RGC grants (Projects 405110 and 404611) and a Direct Grant for Research from the Chinese University of Hong Kong
Article copyright: © Copyright 2015 American Mathematical Society